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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth


Authors: O. Druet and F. Robert
Journal: Proc. Amer. Math. Soc. 134 (2006), 897-908
MSC (2000): Primary 58E30, 58J05, 35J35
Published electronically: September 28, 2005
MathSciNet review: 2180908
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Abstract: We are concerned in this paper with the bubbling phenomenon for nonlinear fourth-order four-dimensional PDE's. The operators in the equations are perturbations of the bi-Laplacian. The nonlinearity is of exponential growth. Such equations arise naturally in statistical physics and geometry. As a consequence of our theorem we get a priori bounds for solutions of our equations.


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Additional Information

O. Druet
Affiliation: Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364 Lyon cedex 7, France
Email: odruet@umpa.ens-lyon.fr

F. Robert
Affiliation: Université de Nice Sophia-Antipolis, Laboratoire J. A. Dieudonné, Parc Valrose, 06108 Nice cedex 2, France
Email: frobert@math.unice.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08330-9
PII: S 0002-9939(05)08330-9
Keywords: Concentration estimates, fourth-order equations, compactness
Received by editor(s): September 29, 2004
Published electronically: September 28, 2005
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.